Answer:
A cease and desist order is handed out by a court and must be followed by the recipient. It orders the recipient to immediately stop doing whatever is included in the cease and desist order. On the other hand, a consent order is a legally binding agreement between two parties. In this case, between the FTC and the company or individual it accuses of wrongdoing.
A consent order is more frequently used by the FTC simply because it is much faster and easier to agree upon something knowing that bad consequences may result from breaching the agreement, than to go to a courthouse to get a cease and desist order. The cease and desist order must be handed out by a judge and that will always take more time.